Direct determination of improved contraction coefficients by a least-squares approach

Abstract

A simple method is presented for the construction of contracted Gaussian basis sets with little or no energy-optimization. The contraction coefficients are fitted by a least-squares procedure to the orbital expansion coefficients of the completely decontracted basis. The method is applied to the construction of minimum basis sets of first-row atoms from (6s, 3p) uncontracted atomic basis sets, and of [6s, 4p] contracted bases from (12s, 8p) uncontracted bases of second-row atoms. The results are better than using the expansion coefficients directly and are usually comparable to fully energy-optimized bases. The method can also be used to generate balanced atomic contraction coefficients from molecular calculations. This is shown with a (7s, 3p) and a (6s, 3p) basis, both contracted to a minimum basis. The contracted basis sets are employed in several small molecules, and the results are compared with calculations done with the decontracted bases and with contracted bases where the contraction coefficients were energy optimized in the molecules.